Oddly enough, one of my sites is for bicycle hire.
The first question to ask yourself is, what phrase would the majority of your customers use? Here, we would say "cycle hire" or "bike hire", but never rental. However, a significant proportion of the customers are from abroad and therefore not native English speakers, and most of these do seem to use the word rental, rather than hire. So the site is optimised for hire (the majority of customers), but also features if rental is used.
On the basis of the Google stats, it would appear that "bike hire" is the more popular phrase for your area and probably the one to go with, but just bear in mind that you're aiming this at real people, if your customers are likely to be atypical. And bear in mind also that you can always tweek things and make adjustments as you go along, as you learn more about both SEO and your visitors.